156 - understanding dynamic random analyses

8/13/2019 156 - Understanding Dynamic Random Analyses

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Dynamic Analyses Understanding Dynamic Random Analyses – Lecture

UnderstandingDynamicRandomAnalyses.mp3

Understanding Dynamic Random Analyses

Dynamic Random Analyses solve random vibration problems with

input in the format of Spectral Density.

Options

Loading

Frequency Dependence

Modes

Damping Coefficient

Output Intervals

Airframe Model

Normal Stress RMS results (psi). (One σ results) Lecture Notes



From a practical perspective, there are a few things to keep in mind: The meanvalue for quantities in this kind of analysis is assumed to be zero. This meansthat the standard deviation (σ) of a quantity is equal to the root mean square(rms). The area underneath a spectral density curve will be the variance or themean square of the quantity. So if the requirements specify that the modelshould be designed based on 3σ stresses define a measure for root-meansquare of the maximum stress and multiply the output by 3.

It is also worth noting that only vector quantities of measures can be reportedin a Dynamic Random analysis. For example, a measure that calculatesdisplacement magnitude or Von Mises stress will not be valid for a DynamicRandom analysis. However, a measure that calculates displacement in the Xdirection or axial stress in the Z direction will be valid.

Understanding Dynamic Random Analyses – Demonstration UnderstandingDynamicRandomAnalyses_demo.mp4

Understanding Dynamic Random Analyses – Procedure Procedure: Understanding Dynamic Random Analyses

ScenarioCreate a Dynamic Random Analysis with tabular input.

CreateDynRandom satellite_frame.asm

Task 1. Open the Mechanica application and create a dynamic random analysis.

1. Click Applications > Mechanica.

2. Click Mechanica Analyses/Studies from the main toolbar.

Every dynamic analysis requires a modal analysis to be defined. Note that

the Modal_Analysis_4_Modes modal analysis has already been defined

for this model.

3. Click File > New Dynamic > Random... from the Analyses and Design Studiesdialog box.

4. In the name field, type Random_Vibration.

5. In the Direction area of the Dynamic Random Analysis Definition dialog box, type

386.4 in the Z field. Verify that the X and Y fields are set to 0.



Because Mechanica does not use “g” as a unit, you typed the value of g as

the base excitation (in in/s2).

6. In the Damping Coefficient (%) area on the Modes tab, verify that the drop-down

menu is set to For all modes and type 4 in the field below the drop-down menu.

The dialog box should now appear as shown in the figure.

This value is applied as a 4% damping coefficient.

7. Click Function to open the Functions dialog box.

8. Click New... to being creating a new function.



The PSD acceleration for this analysis is given by the following table:

Frequency (Hz) Acceleration PSD (g2/Hz)

20 0.0256

20–50 +6 dB/octave

50 0.16

800 0.16

800–2000 -4.5 dB/octave

2000 0.0256

9. In the Definition area of the dialog box, select Table from the drop-down menu.

10. Click Add Row, verify that the Start at field is set to 1, set the Num Rows field to

4 and click OK.

11. Populate the table as shown in the figure. Be sure to select Logarithmic and

Logarithmic for each of the drop-down menus at the bottom of the dialog box.



Changing to the logarithmic scale is critical because the table above

indicates that the slope for 20-50Hz and 800-2000Hz is on a logarithmic

scale. PSD function slopes defined as a specific dB/octave value are

common.

12. Click Review..., verify that the Lower Limit is set to 20 and the Upper Limit is setto 2000 and click Graph.

13. Once the graph is displayed in the Graphtool dialog box, click Format > Graph.

14. If necessary, select the Y Axis tab and select the Log Scale check box.

15. Select the X Axis tab and select the Log Scale check box.

16. Click OK to close the Graph Window Options dialog box and display the graph.

17. When you are finished reviewing the graph, click File > Exit > Done > OK > OK

to complete defining the function and return to the Dynamic Random Analysisdialog box.



18. Select the Output tab in the dialog box, select the Full RMS Results for

Displacements and Stresses check box, and type 20 in the Minimum Frequencyfield.

19. In the Maximum Frequency area, select the User-defined radio button and type2000 in the field as shown in the figure.

20. Click OK to complete the dynamic random analysis definition and close the dialog

box.

21. Return to the Standard Pro/ENGINEER mode by clicking Applications >Standard.

22. Click Save from the main toolbar and click OK to save the model.

23. Click File > Close Window from the main menu.

24. Click File > Erase > Not Displayed > OK to erase the model from memory.

This completes the procedure.

Understanding Dynamic Random Analyses – Exercise Exercise: Running a Dynamic Random Analysis

Objectives

After successfully completing this exercise, you will be able to:

Understand the different settings in a dynamic random analysis.

Type data presented as g2 /Hz into a dynamic random analysis.

Create valid measures for a dynamic random analysis.



ScenarioRandom analysis occurs in a number of applications. A satellite enclosed in a launch

vehicle is subject to random vibration during launch, as is an airplane when it encounters

turbulence or an off-road vehicle on uneven ground.

In this exercise, the wing of an aircraft will be analyzed for random vibration. The input

will be presented in a format and units common for this kind of problem. The input willalmost always be expressed in terms of base excitation, and the units for the spectraldensity of acceleration will almost always be in g2 /Hz. In addition, transition between

values at different frequencies will almost always be logarithmic.

Creating measures for a dynamic random analysis will be reviewed. Though a Dynamic

Random Analysis outputs quantities in spectral density, how to use the output to

determine confidence in the model will be examined.

The input for this model is specified by the table and graph below. Acceleration data for

dynamic random analysis is often obtained from empirical data. In addition, several large

institutions such as the US Army or NASA have public documents (for example, MIL-STD-

810) that include PSD Acceleration plots to be used for products designed for them. It isalso not uncommon for consumer products marketed as “rugged” or “heavy duty” to be

designed using the types of specifications.

Frequency

(Hz)

Acceleration

(g2 /Hz)

20 0.075

100 0.1

400 0.1

600 0.03

Note how the chart provided is on a log scale for both axes, and the

curve appears as straight lines. This means that when the table is

typed in Mechanica, Logarithmic interpolation has to be used.

Sometimes if a graph is not included, the slope information will be



included in the table in the form of dB/octave. Setting the

interpolation to Logarithmic will account for this as well.

DynRandExer wing_rgt.prt

Task 1. Open the Mechanica application and begin creating a dynamic randomevaluation.

1. Click Applications > Mechanica.

Note that the units for this model are in-lbf-s and that the model already has

a material assignment (Aluminum 6061), simulation features (4 points), and

constraints (on the inboard section of the wing).


Note that a modal analysis has already been created. The modal analysis

calculates the first six modes of vibration for WING_RGT.PRT.

3. In the Analyses and Design Studies dialog box, click File > New Dynamic >

Random....

4. Type Random_Vibration in the Name field.

The direction vector for base excitation has served as a scaling factor in

other dynamic analyses. In Dynamic Random analyses, the values typed into

the base excitation vector are squared and then scaled by the function

defined. So if the acceleration is reported in g2 /Hz, then the base excitation

vector should only have the value of g for that system of units, not g2. As

such, for this model the acceleration of gravity in in/s2 is 386.4.

5. Type 386.4 in the Y field as shown in the figure.

6. Select the Supports radio button in the Relative to field.



7. In the Damping Coefficient area of the dialog box, verify that the drop-down menu

is set to For all modes and type 5 in the second field as shown in the figure.

8. In the Frequency Dependence area of the dialog box, click Function .

9. Click New... in the Functions dialog box.

Note the default PsdFunc1 name for the function.

10. Select Table from the Definition drop-down menu.

11. Click Add Row, verify the Start at field is set to 1, type 4 in the Num Rows field,and click OK.

12. Populate the table as shown in the figure.

13. Select Logarithmic for both of the drop-down menus at the bottom of the dialog

box as shown in the figure.

14. Click OK > OK to finish creating the function and return to the Dynamic Random

Analysis dialog box.



15. Select the Previous Analysis tab.

Note how the previously defined Modal_Analysis_6_modes is

automatically selected at the Modal Analysis. This is due to the fact that it is

the only modal analysis currently in the working directory.

16. Select the Output tab.

17. Select the Full RMS Results for Displacements and Stresses check box as

shown in the figure.

18. Select the Mass Participation Factors check box as shown in the figure.

19. In the Output Intervals area of the dialog box, verify that the drop-down menu isset to Automatic Intervals within Range as shown in the figure.

20. Type 20 in the Minimum Frequency field as shown in the figure.

21. In the Maximum Frequency area, select the User-defined radio button and type

600 in the field as shown in the figure.

22. The dialog box should now appear as shown in the figure. Click OK to completethe Dynamic Random Analysis definition and close the dialog box.



Task 2. Create valid measures for the dynamic random analysis.

Measures that are valid for a dynamic random analysis have to fulfill two

requirements:

A. They must be associated with specific points on the model.

B. They must be vector quantities. (For instance acceleration magnitudeis not valid, but acceleration in the x direction is valid.)

1. Click Close in the Analysis and Design Studies dialog box.

2. Click Simulation Measure from the Mechanica toolbar and click New in the

Measures dialog box.



3. Type acceleration_y_tip in the Name field.

4. From the Quantity drop-down menu, select Acceleration.

5. From the Component drop-down menu, select Y.

6. Verify that the Coordinate system is set to WCS.

7. In the Spatial Evaluation area of the dialog box, select At Point from the first

drop-down menu.

8. Click Select Reference and select PNT14 from the model as shown in the

figure.

9. In the Dynamic Evaluation field, select At Each Step from the first drop-down

menu.

10. The dialog box should now appear as shown in the figure. Click OK to completethe Measure Definition and close the dialog box.



11. Click Copy in the Measures dialog box.

12. Select PNT14 from the model and click OK in the Multiple Measure Copy dialogbox.

13. If necessary, select the acceleration_y_tip1 and click Edit.

14. Edit the Name field to acceleration_y_tip_rms.

15. In the Dynamic Evaluation field, select RMS from the drop-down menu.

16. The dialog box should now appear as shown in the figure. Click OK to complete

the Measure Definition and close the dialog box.

17. Click Close to close the Measures dialog box.



Task 3. Run the dynamic random analysis and review the results.


2. Select the Random_Vibration analysis from the Analyses and Design Studies list

and click Start Run > Yes to start the design study.

3. Click Display Study Status once the analysis is started.

The analysis should take a few minutes to complete.

4. When the analysis is complete, review the Diagnostics and Run Status window.

Click Close to close each one when you are through reviewing it.

5. Verify that Random_Vibration is selected in the Analyses and Design Studies

dialog box and click Results to start Results mode.

6. Select Graph from the Display type drop-down menu.

7. In the Graph Ordinate (Vertical) Axis area (on the Quantity tab), select Measure

from the first drop-down menu.



8. Click Define Measure to open the Measures dialog box.

9. Select acceleration_y_tip from the User-Defined list of measures, and click OK.

10. The dialog box should appear as shown. Click OK and Show to show the graph

result.

11. Review the graph. Note that your display might be slightly different, depending on

which exercises you have completed from this course.

When a quantity reaches high values when it encounters a natural mode, it

can be more convenient to display the graph on a log-log scale to be able to

see more information. You will do this in the next few steps.

12. From the Results window main toolbar, click Format > Graph.



13. Verify that the window is showing information on the Y Axis and select the Log

Scale check box in the lower-right corner of the dialog box as shown in the figure.

14. Select the X Axis tab, and select the Log Scale check box in the lower-right

corner of the dialog box as shown in the figure.

15. Click OK to view the graph in log-log format.

Note that this is the spectral density for the acceleration. The units for the y-

axis are in2 /s2Hz, not g2 /Hz

16. Click Delete Selected Definition from the Results window main toolbar.

17. From the Results Mode main toolbar, click Result Window .

18. Select Random_Vibration and click Open.

19. Type XX in the Title field.

20. Verify that the Display type drop-down menu is set to Fringe.



21. On the Quantity tab, select Stress from the first drop-down menu as shown in the

figure.

22. If necessary, set the Component drop-down menu on the Quantity tab to XX.

Note that there is no Von Mises stress available—it is not calculated for a

dynamic random analysis.

23. Click OK and Show to show the Fringe plot result.

24. Click Copy from the main toolbar in the Results window.

25. Edit the title field to read YY.

26. Select YY from the second drop-down menu on the Quantity tab.


28. Click Copy from the main toolbar in the Results window.

29. Edit the title field to read ZZ.

30. Select ZZ from the second drop-down menu on the Quantity tab.


32. Review the resulting fringe plots.

The highest of the axial stresses appears to be 1,081 psi in the Z direction.

Note that the values of stress reported here are the root mean square (RMS)

stresses, not the actual stress on the model at any point in time. It is

assumed that since the vibration is naturally occurring, it follows a normal

probability distribution function and has a mean of zero. If the mean is equal

to zero, then the root mean square is equal to the standard deviation (sigma

or σ). One way you can use this to judge results for random vibration is to

use “three sigma” results. It is believed that there is a 0.3% probability that

the value could be higher than three standard deviations. So for your stress

of 1,081 psi, the three-sigma value would be 3,243 psi. This means there is

only a 0.3% chance that the axial stress will be higher than 3,243 psi. This

is well below the yield stress for Aluminium 6061, which is 40,000 psi.



33. When you are finished reviewing the results, click File > Exit Results > No toexit the Result window without saving any results.

34. Return to the Standard Pro/ENGINEER mode by clicking Applications >Standard.

35. Click Save from the main toolbar and click OK to save the model.

36. Click File > Close Window from the main menu.

37. Click File > Erase > Not Displayed > OK to erase the model from memory.

This completes the exercise.

156 - understanding dynamic random analyses

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